why does scikitlearn says F1 score is ill-defined with FN bigger than 0?

I run a python program that calls sklearn.metrics's methods to calculate precision and F1 score. Here is the output when there is no predicted sample:

/xxx/py2-scikit-learn/0.15.2-comp6/lib/python2.6/site-packages/sklearn/metr\
ics/metrics.py:1771: UndefinedMetricWarning: Precision is ill-defined and being set to 0.0 due to no predicted samples.
  'precision', 'predicted', average, warn_for)

/xxx/py2-scikit-learn/0.15.2-comp6/lib/python2.6/site-packages/sklearn/metr\
ics/metrics.py:1771: UndefinedMetricWarning: F-score is ill-defined and being set to 0.0 due to no predicted samples.
  'precision', 'predicted', average, warn_for)

When there is no predicted sample, it means that TP+FP is 0, so

• precision (defined as TP/(TP+FP)) is 0/0, not defined,
• F1 score (defined as 2TP/(2TP+FP+FN)) is 0 if FN is not zero.

In my case, sklearn.metrics also returns the accuracy as 0.8, and recall as 0. So FN is not zero.

But why does scikilearn says F1 is ill-defined?

What is the definition of F1 used by Scikilearn?

Solution 1:

https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/metrics/classification.py

F1 = 2 * (precision * recall) / (precision + recall)

precision = TP/(TP+FP) as you've just said if predictor doesn't predicts positive class at all - precision is 0.

recall = TP/(TP+FN), in case if predictor doesn't predict positive class - TP is 0 - recall is 0.

So now you are dividing 0/0.

Solution 2:

Precision, Recall, F1-score and Accuracy calculation

- In a given image of Dogs and Cats

  * Total Dogs - 12  D = 12
  * Total Cats - 8   C = 8

- Computer program predicts

  * Dogs - 8  
    5 are actually Dogs   T.P = 5
    3 are not             F.P = 3    
  * Cats - 12
    6 are actually Cats   T.N = 6 
    6 are not             F.N = 6

- Calculation

  * Precision = T.P / (T.P + F.P) => 5 / (5 + 3)
  * Recall    = T.P / D           => 5 / 12

  * F1 = 2 * (Precision * Recall) / (Precision + Recall)
  * F1 = 0.5

  * Accuracy = T.P + T.N / P + N
  * Accuracy = 0.55

Wikipedia reference